For extra fun, groups of student in a class are tasked to create algebraic expression to satisfy the measures of the angles of their triangular picture frame project. If the measure of the angles are as follows:m∠A = 5x - 3, m∠C = 2x + 5, m∠E = 3x - 2, arrange the sides of the frame in increasing order. don't spam!! ​

Step-by-step explanation:

Sum of all angles of the triangle = 180

∠A + ∠C + ∠E = 180

5x - 3 + 2x +5 + 3x -2 = 180

Combine like terms

5x + 2x + 3x - 3 + 5 - 2 = 180

            10x + 0 = 180

10x = 180

Divide both sides by 10

x = 180/10

x = 18

∠A = 5x - 3 = 5*18 - 3 = 90 - 3 = 87

∠C = 2x +5 = 2*18 + 5 = 36 + 5 = 41

∠E = 3x - 2 = 3*18 - 2  = 54 - 2 = 52

Side opposite to smallest angle is small

∠C is smallest. So, AE is smallest side

Next smallest is ∠E. So, AC is the next side

AE < AC < CE

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.